Folding Theory Applied to Residuated Lattices

1Departmen of Mathematics, University of Yaounde 1, P.O. Box 812, Yaounde, Cameroon2Departmen of Mathematics, University of Dschang, P.O. Box 67, Dschang, Cameroon3Departmen of Mathematics, University of Oregon, Eugene, OR 97403, USA

Received 14 February 2014; Revised 20 April 2014; Accepted 20 May 2014; Published 25 June 2014

Abstract

Residuated lattices play an important role in the study of fuzzy logic based on -norms. In this paper, we introduce some notions of -fold filters in residuated lattices, study the relations among them, and compare them with prime, maximal and primary, filters. This work generalizes existing results in BL-algebras and residuated lattices, most notably the works of Lele et al., Motamed et al., Haveski et al., Borzooei et al., Van Gasse et al., Kondo et al., Turunen et al., and Borumand Saeid et al., we draw diagrams summarizing the relations between different types of -fold filters and -fold residuated lattices.